2026ApJ...998..155X

The third body is expected to shape the formation and evolution of close binary systems. In this work, we develop a method to detect and characterize the tertiary companion around eclipsing binaries through the combined analysis of eclipse timing variation, Hipparcos, and/or Gaia astrometry. This method allows us to determine both the true mass and the inclination of the tertiary body that inferred from light-travel time effect. For the massive B-type binary V Pup, we do not confirm the previously reported 5.47 yr signal; instead, we identify a longer period of 14 yr. The orbital semimajor axis and mass of the outer body are revised to ${a}_{C}={17.88}_{-0.15}^{+0.15}$ au and ${M}_{C}={7.73}_{-0.14}^{+0.14}\,{M}_{\odot }$, confirming it as a promising stellar-mass black-hole candidate for further follow-up study. For the tertiary of the contact binary CY Ari, we obtain ${P}_{C}=5.40{6}_{-0.016}^{+0.017}$yr, ${e}_{C}=0.52{6}_{-0.027}^{+0.032}$, ${I}_{C}={85.6}_{-6.5}^{+7.8}$ °, and a true mass of ${M}_{C}=0.64{0}_{-0.029}^{+0.029}\,{M}_{\odot }$, supporting the white dwarf hypothesis proposed in previous study. The orbits of both systems are nearly edge-on (I = 90°), implying that they may form in a coplanar environment. We highlight the advantages of our method for detecting dark companions in binary and triple systems.